Preheat the oven to 400°F. Unroll the puff pastry sheet onto a parchment lined sheet pan. With a sharp knife score the puff pastry about 2 cm inside the edges to create a border.
Sprinkle ¾ of the goat cheese crumble inside the border of the puff pastry.
Arrange the pears in a line slightly overlapping each other starting from one edge to the other. Repeat with a second and third row of pears, alternating the direction of your rows.
In a small bowl whisk together 2 tablespoons of water, a pinch of salt and the egg to create an egg wash. Gently brush the edges of the puff pastry with the egg wash. (This step is optional, see note.)
Bake the puff pastry for 15-20 minutes until the edges are puffed and browned.
Sprinkle the tart with the remaining goat cheese, arugula, and pomegranate seeds.
Mix together the honey and balsamic vinegar and drizzle it over the top of the tart. Cut and serve.